Mentally Prepping Students for Exams

When it comes to high-stakes assessments, I feel the biggest part of my job is to prepare my students mentally, as opposed to mathematically. I know, there's a lot of overlap, in fact it probably is mostly overlap. But I think that without that affective aspect of preparation, it really doesn't matter how good they are at mathing.

It's stressful writing these things, and the biggest stress-busting window of opportunity is only open before the exam. As in sportsball games, a great deal of the result is really determined during practice and preparation. Since I teach high school students, that part is my job too. It's not enough that I do a good job teaching stuff, or that I spend a period or two reviewing stuff - I have to accompany them on their mental preparation as well.

What I want to do BEFORE the exam is to actively, in a structured and gradually empowering way, help them:

• practice retrieving information
• organize all that math info in their minds to enable retrieval
• know what to expect on the day of the exam
• become fluid with certain types of questions that are likely to be on the exam (note -  if I'm the author of the exam I probably give a lot away here - if anyone's paying attention it can pay off for them big time)
• try questions that they've never seen before but for which they nevertheless have all the tools they need
• come up with strategies to handle questions like the aforementioned
• practice pacing themselves
• develop independence and confidence

There are, of course, some kids who don't need me to do this, who always do well and don't even need to spend much time studying, but my instincts, and my results, tell me that those students are in the minority. Most either don't know how to digest and use large amounts of info, or aren't motivated to spend the time preparing. They're my students too, and I refuse to simply shrug my shoulders and write them off as not having what it takes. If it's motivation they're lacking, that's also my job.

And if there are students whose only preparation takes place during class with me, I at least want to make sure that time counts for SOMETHING.

What I did this year: Outside of class

Review VoiceThreads: Review started outside of class. I didn't want to spend class time going over the basics, so for that I made review VoiceThreads. Here's a sample for the optimization unit.

These asynchronous reviews covered the procedures, examples, vocabulary, notation, and summarized all the stuff they've seen before, which is theoretically already in their notes. Some kids will have already looked that over, or won't even need to, but again, they're in the minority, so for the rest, I do this. This way, the kids who are ready to practice don't have to sit and listen to me blather endlessly during class, but the kids who need the refresher have it there. Do they all do it? Nope. But it's there for those who are motivated and who need it. Am I doing too much? That's another blog post. Also no. These are kids and this is a hard course.

Sidenote: For the reviews on functions, my voicethreads gradually form a sequence as the year goes on, because I keep adding to each one as we study new functions. I use a structure I call the Wheel of Functions. Here's the most recent one, with 4 functions in it:


It's a kind of scaffolding that I think makes it easier to see connections, to get the big picture, and compare the properties of different functions. This hits the organizing of large amounts of info, which helps with the retrieval practice.

Review Packages: It's not enough to consume of course - math is about doing, so the next thing they get is review packages, which are made up of actual exam questions. I realize this is what most people do. (Organizing a decade or so of these questions and keeping track of which ones I've used...that's a whole other thing...) These are to be handed in, so everyone has to at least try these questions. I give a mark, but it's based on 3 things only: Handing it in on time, trying every question, and showing all reasoning for each question. So even if you're not ready to correctly do these questions, you can get a good "mark" because you're starting to prepare yourself. Does everyone do this? Pretty much. It's either a wake-up call to start working (in a shock-therapy kind of way) or it's a good indication of where to focus one's attention. At the very least it hits the knowing-what-to-expect benchmark.

During class: Snappers, Zingers, and Deep Dives

A combination of quick-to-answer and not-so-quick questions that everybody gets to try:

Snappers: You have to walk before you can run. I start a class with 4-5 easy questions (Eg which function needs 2 templates OR Simplify the rule y = 10 + 3^2x OR write this as a constraint) that they can answer in 1-2 minutes, then send me their answer by private message, and if they don't know the answer, then that's what they pm me. Once I've heard from all, we immediately go over it, then if needed we do another one just like it, immediately. End result: retrieval practice, exposure to the very least of what's expected, motivation - they are super motivated and capable to get it right the second time, encouragement, practice with pacing, also sets up next day's review. Also - hopefully this causes some to take to those review voicethreads if they haven't already!

Zingers: When it's closer to exam time, fewer questions. Same structure as snappers but these take a little more time. These questions may just take longer because there are more steps, or they may use some of the ideas we went over in the snappers. Again, if needed, do another one right away. End results: Exposure to next level, more pacing practice, more fluidity, also communicates subtly that maybe they should pay attention to the exact things I'm reviewing now because there's probably a good reason I'm focusing on it...

Deeper dive: These I weave in between the snappers and the zingers.This is where we really get into it:

1. Revealing hidden layers - like that fact that in this course, we end up solving systems of equations very often, even though it's not actually part of the course. We solve a system to:
• express a vector as a linear combination of other vectors
• to find two missing parameters of a function
• to find the coordinates of the vertices of a polygon of constraints. It's everywhere.
2. Reviewing certain types of multi-step questions that typically show up, like piecewise functions. We took another look at actual test questions that they've already done, along with the full solutions, and if time, give them another one to try right then and there.
3. Trying those questions they've never seen before, and for which they have all the tools
4. Going over strategies to deal with those questions they've never seen before, to identify the tools they need to mobilize

Overall: Variety Really Matters

I try really hard to fit as much variety in the voicethreads, review packages, snappers, zingers, and deep dives as possible so that by the time the exam happens, their brains have truly been stretched and warmed up for the race. Those that did it all are really ready, and those that did only the minimum have at least a chance.

Today they wrote their exam, and tomorrow they write the second.

Fingers fervently crossed.

Exponent Mindfulness

In preparation for our exponential/logarithmic function unit, I decided to try something I called  Exponent Mindfulness. Mindfulness because that's an initiative the team I work with has been working on, and exponents because being able to not only evaluate expressions involving them, but recognising numbers as powers, is the key to this whole unit. After all, working exponents out backwards is what logs are all about.

First we spent a week on Exponent Boot Camp, in which I review WHAT the exponent properties are, and also WHY they are, including negative exponents, rational exponents, and rational bases with positive and negative exponents. That covered the first part - evaluating expressions with all kinds of bases and exponents.

On this day, however, it was all about going the other way, developing those exponent lenses. After warming up with a few evaluation examples, I put 16 on the board and asked how can we write this number as a power? The answers I got were as expected:

Then I asked - that's it right? No other possibilities? Waited and asked about the possibility of a negative exponent. Here's where things got interesting. Even though everyone was fine moments ago with how to figure out a fraction to a negative exponent, the idea that you can get 16 from a negative exponent suddenly seemed to be mind bending. (It's always more fun to give your students the answer and ask them to come up with the question.)

Anyway, so I showed them this:

We spent a few minutes working out each of these, just to re-convince everyone that these were in fact all equal to 16.

Back to 16, and I asked again, "That's it now, right? No other possibilities?"

My students know me well enough to know that answer to that. So we moved on to rational exponents:

I got a few really great answers added here, like 65536^(1/4) and 1048576^(1/5).

Me: So that's it right?

Students: Nope, that's never it is it?

So now that we all knew that there were in fact infinitely many ways to express a number as a power,  I asked everyone to write a power on the board that equals 81, specifying that you can't use one that's already there. That went really well. Definitely you should do this again next year Future Audrey.